
%% bare_conf.tex
%% V1.3
%% 2007/01/11
%% by Michael Shell
%% See:
%% http://www.michaelshell.org/
%% for current contact information.
%%
%% This is a skeleton file demonstrating the use of IEEEtran.cls
%% (requires IEEEtran.cls version 1.7 or later) with an IEEE conference paper.
%%
%% Support sites:
%% http://www.michaelshell.org/tex/ieeetran/
%% http://www.ctan.org/tex-archive/macros/latex/contrib/IEEEtran/
%% and
%% http://www.ieee.org/

%%*************************************************************************
%% Legal Notice:
%% This code is offered as-is without any warranty either expressed or
%% implied; without even the implied warranty of MERCHANTABILITY or
%% FITNESS FOR A PARTICULAR PURPOSE! 
%% User assumes all risk.
%% In no event shall IEEE or any contributor to this code be liable for
%% any damages or losses, including, but not limited to, incidental,
%% consequential, or any other damages, resulting from the use or misuse
%% of any information contained here.
%%
%% All comments are the opinions of their respective authors and are not
%% necessarily endorsed by the IEEE.
%%
%% This work is distributed under the LaTeX Project Public License (LPPL)
%% ( http://www.latex-project.org/ ) version 1.3, and may be freely used,
%% distributed and modified. A copy of the LPPL, version 1.3, is included
%% in the base LaTeX documentation of all distributions of LaTeX released
%% 2003/12/01 or later.
%% Retain all contribution notices and credits.
%% ** Modified files should be clearly indicated as such, including  **
%% ** renaming them and changing author support contact information. **
%%
%% File list of work: IEEEtran.cls, IEEEtran_HOWTO.pdf, bare_adv.tex,
%%                    bare_conf.tex, bare_jrnl.tex, bare_jrnl_compsoc.tex
%%*************************************************************************

% *** Authors should verify (and, if needed, correct) their LaTeX system  ***
% *** with the testflow diagnostic prior to trusting their LaTeX platform ***
% *** with production work. IEEE's font choices can trigger bugs that do  ***
% *** not appear when using other class files.                            ***
% The testflow support page is at:
% http://www.michaelshell.org/tex/testflow/



% Note that the a4paper option is mainly intended so that authors in
% countries using A4 can easily print to A4 and see how their papers will
% look in print - the typesetting of the document will not typically be
% affected with changes in paper size (but the bottom and side margins will).
% Use the testflow package mentioned above to verify correct handling of
% both paper sizes by the user's LaTeX system.
%
% Also note that the "draftcls" or "draftclsnofoot", not "draft", option
% should be used if it is desired that the figures are to be displayed in
% draft mode.
%
\documentclass[conference]{IEEEtran}
% Add the compsoc option for Computer Society conferences.
%
% If IEEEtran.cls has not been installed into the LaTeX system files,
% manually specify the path to it like:
% \documentclass[conference]{../sty/IEEEtran}


\usepackage[cmex10]{amsmath}
\usepackage{footnote}
\usepackage{amsmath, amsthm, amssymb, amscd}
\usepackage[lined,linesnumbered,ruled]{algorithm2e}
\usepackage{ifthen}
\usepackage{cite}
\usepackage{graphicx}
\usepackage{epsfig}
\usepackage{subfig}

\usepackage{bibspacing}
\setlength{\bibspacing}{\baselineskip}

\newtheorem{Lemma}{Lemma} 
\newtheorem*{Lemmaprev}{Lemma 4}
\newtheorem{Property}{Property} 
\newtheorem{Theorem}{Theorem} 
\newtheorem{Corollary}{Corollary} 
\newtheorem{Definition}{Definition} 
\newtheorem{Observation}{Observation} 
\newtheorem{Example}{Example}


\newcommand{\suc}{\operatorname{succ}}
\newcommand{\Scurr}{\operatorname{S_{curr}}}
\newcommand{\Stage}{\operatorname{Stage}}
\newcommand{\nStage}{\operatorname{newStage}}
\newcommand{\Cmin}{\operatorname{C_{min}}}
\newcommand{\vsrc}{\operatorname{v_{src}}}
\newcommand{\pred}{\operatorname{pred}}

\begin{document}
\title{Bare Demo of IEEEtran.cls for Conferences}

\author{\IEEEauthorblockN{Michael Shell}
\IEEEauthorblockA{School of Electrical and\\Computer Engineering\\
Georgia Institute of Technology\\
Atlanta, Georgia 30332--0250\\
Email: http://www.michaelshell.org/contact.html}
\and
\IEEEauthorblockN{Homer Simpson}
\IEEEauthorblockA{Twentieth Century Fox\\
Springfield, USA\\
Email: homer@thesimpsons.com}
\and
\IEEEauthorblockN{James Kirk\\ and Montgomery Scott}
\IEEEauthorblockA{Starfleet Academy\\
San Francisco, California 96678-2391\\
Telephone: (800) 555--1212\\
Fax: (888) 555--1212}}

% make the title area
\maketitle


\begin{abstract}
The abstract goes here.
\end{abstract}

\IEEEpeerreviewmaketitle



\section{Introduction}
Introduction goes here.

\section{System Model}
Model goes here.

\section{Our Text Work-In-Progress}

\subsection{Server graph algorithm}
In this section, we describe our algorithm to create a server graph for a given execution path graph. This algorithm uses some notations which are listed below:
\begin{itemize}
	\item $A \otimes B$. All the nodes $v_k \in A$ whose $\suc\left\{v_k\right\}=\emptyset$ are connected to all the nodes in $B$.
	\item $\Stage(i, G)$. Set of nodes $v_k \in G$ such that the longest path from $\vsrc$ to $v_k$ is of length $i$.
\end{itemize}

The pseudo-code of the server graph creation algorithm is shown in Algorithm~\ref{fig:sgcreate}.
\begin{algorithm}[h]
\footnotesize
\SetKwInOut{Input}{Input}\SetKwInOut{Output}{Output}
   \Input{$G.$ A copy of the execution path graph}
   \Output{$G'.$ A server graph corresponding to the input graph $G$}
	 $G' \longleftarrow \emptyset; \Scurr \longleftarrow \emptyset; i \longleftarrow 0$\\
	 \While{$\left(G \neq \emptyset\right)$}
	 {
	   %$\Scurr \longleftarrow \Scurr \cup \Stage(i, G)$\\
		 $\Scurr \longleftarrow$ all the nodes $v_k \in G$ such that $\pred\left(v_k\right) = \emptyset$\\
		 $\Cmin \longleftarrow \min\left\{C_k | v_k \in \Scurr\right\}$\\
		 $\nStage \longleftarrow$ set of $\left|\Scurr\right|$ nodes $v_k$ with $C_k = \Cmin$\\
		 $ G' \longleftarrow G' \otimes \nStage$\\
		 \ForEach{$\left(v_k \in G \text{ such that } v_k \in \Scurr\right)$}
		 {
		   $C_k \longleftarrow C_k - \Cmin$\\
			 \If{$\left(C_k = 0\right)$}
			 {
			   $G' \longleftarrow G' \setminus \left\{v_k\right\}$
			 }
		 }
		 $i \longleftarrow i + 1$
	 }
	 return $G'$
\caption{CreateG: An algorithm to convert a graph of an execution path into a server graph.}
\label{fig:sgcreate}
\normalsize
\end{algorithm}

We now prove some useful properties about the server graph creation algorithm.
\begin{Lemma}
$WL(G') = WL(G)$
\end{Lemma}
\begin{proof}
At each iteration of the $\mathrm{while}$ loop in Algorithm~\ref{fig:sgcreate}, $\left|\Scurr\right| \times \Cmin$ units of workload is added to $G'$ (see line~5 and line~6) and $\left|\Scurr\right| \times \Cmin$ units of workload is subtracted from $G$ (see line~5 and line~6). From this and the condition of the $\mathrm{while}$ loop, the claim trivially holds.
\end{proof}

\section{Conclusion}
The conclusion goes here.




% conference papers do not normally have an appendix


% use section* for acknowledgement
\section*{Acknowledgment}


The authors would like to thank...





% trigger a \newpage just before the given reference
% number - used to balance the columns on the last page
% adjust value as needed - may need to be readjusted if
% the document is modified later
%\IEEEtriggeratref{8}
% The "triggered" command can be changed if desired:
%\IEEEtriggercmd{\enlargethispage{-5in}}

% references section

% can use a bibliography generated by BibTeX as a .bbl file
% BibTeX documentation can be easily obtained at:
% http://www.ctan.org/tex-archive/biblio/bibtex/contrib/doc/
% The IEEEtran BibTeX style support page is at:
% http://www.michaelshell.org/tex/ieeetran/bibtex/
%\bibliographystyle{IEEEtran}
% argument is your BibTeX string definitions and bibliography database(s)
%\bibliography{IEEEabrv,../bib/paper}
%
% <OR> manually copy in the resultant .bbl file
% set second argument of \begin to the number of references
% (used to reserve space for the reference number labels box)
\begin{thebibliography}{1}

\bibitem{IEEEhowto:kopka}
H.~Kopka and P.~W. Daly, \emph{A Guide to \LaTeX}, 3rd~ed.\hskip 1em plus
  0.5em minus 0.4em\relax Harlow, England: Addison-Wesley, 1999.

\end{thebibliography}




% that's all folks
\end{document}


